Geometric (Berry) phases and statistical transmutation in the two-dimensional systems of antiferromagnetically correlated electrons

Focusing on the hole-doped two-dimensional systems of strongly correlated e lectrons, we examine the geometric phases which arise as a result of polaro n transport around closed loops. It is of interest to see differences in th e geometric phases between the two different systems of antiferromagnets, t he Ising antiferromagnets and the Heisenberg antiferromagnets. For this stu dy we apply the Lanczos exact diagonalization method to the Holstein-Hub ba rd, Holstein-tJ, and Holstein-tJ(z) models. It is shown from this study tha t the transverse spin interactions (fluctuations) are responsible for the g eneration of non-trivial geometric phases for the Heisenberg antiferromagne ts, unlike the case of the Ising antiferromagnets. (C) 2001 Elsevier Scienc e B.V. All rights reserved.